under Paper UI --> Add-ons MQTT Binding along with MQTT Persistence are installed
Problem: mqtt binding is not showing up under Configuration --> Bindings
I restarted openhab, I also edited mqtt.cfg to add the broker IP, ID, user name, and password, but all this did not help to show the binding in Configuration --> Bindings
The PaperUI Configuration>Bindings only shows native openHAB 2 bindings. As the mqtt binding is version 1.9, it will not show up here. As long as it is installed (i.e. you see it in the Add-ons page as per your screenshot) and you have correctly configured the services/mqtt.cfg file, it should work fine.
Unfortunately as I use text files for configuration, I am not really familiar with how to set up items via paperUI. If you do use text files yourself, you will find examples on the mqtt binding documentation page - https://github.com/openhab/openhab1-addons/wiki/MQTT-Binding.
This is really difficult for new users. I assumed that things like this are managed by the PaperUI. I assume this is coming, but man this is hard on new users. A note in the documentation would help … however: I installed the embedded MQTT broker, that I never got to work, but when I did, the configuration for the binding did appear in the PaperUI.